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The hidden gravity Enbang Li1 1 School of Physics, Faculty of Engineering and Information Sciences, University of Wollongong, Wollongong, NSW 2522 Australia Newton’s law of universal gravitation states that the attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them [1]. In the real world, no ideal point mass exists, but rather all physical objects are of distributed masses. Therefore, attentions need to be paid when Newton’s gravity law is applied. According to Newton’s theorems on gravitation, an ellipsoidally symmetric mass distribution can be simplified to a point mass [2]. As a special case, a spherical mass distribution satisfies the condition required by the theorems, and also can be further treated as a point source (with its total mass) located in its centre for both near-field and far-field situations. However, for nonspherical mass distributions, this statement holds only for the far-field and could become invalid for the near-field. The variations of gravitational forces will become more obvious with the increase of the oblateness or flatness of the mass distribution. The extreme case is a disk-like mass distribution, as shown in Fig.1c&d. In the vicinity of the disk edge, 𝑘𝑔 can reach values which are much larger than 1, depending on the distance from the disk edge. For a case where the distance is 0.01% of the disk radius (R), 𝑘𝑔 reaches 6. This means that a particle locating at that point will experience a gravitational force which is more than 6 times stronger than that generated by a point source with the same mass locating at the centre of the disk. In other words, a disk of mass M acting on a particle at the disk edge is equivalent to a spherically distributed mass of 6M. More detailed calculations show that when the distance between the particle and the disk edge is further reduced, 𝑘𝑔 will increase more rapidly. Here we study the near-field gravitational forces generated by non-spherical mass distributions for various shapes and discover that the near-field gravitational force distributions strongly depend on the mass distributions and can significantly deviate from those generated by spherical mass-distributions. Galaxies all have very different shapes, from ellipticals, spirals, barred spirals, to irregular galaxies, and their mass distributions, in most cases, are complex and significantly different from spherical. The additional gravitational forces generated by non-spherical mass distributions, or hidden gravity, could have significant implications for kinematics of the cosmic structures. . Shown in Fig.1 are the calculated gravitational force distributions for two different mass distributions: an oblate spheroid and a disk. For comparison purpose, the calculated gravitational forces are normalized by that generated from a simplified point mass which is equivalent to a spherical mass distribution. Plotted in Fig.1 are values of a factor 𝑘𝑔 defined as 𝑘𝑔 = 𝐹/𝐹0 , where F is the gravitational force between the test mass m and the distributed mass with a total mass of M; and 𝐹0 is the gravitational force between the test mass m and the simplified point mass M. Therefore, for a non-spherical mass distribution, 𝑘𝑔 represents how much the gravitational force deviates from that generated by a spherical mass-distribution. It can be easily verified that for a spherical mass distribution, 𝑘𝑔 is constantly unity in the space out of the distributed mass, both in near- and far-field conditions. For the oblate spheroid or revolving ellipsoid (the length of semi-minor axis is half of that of semi-major axis, R) mass distribution considered here, it is clear that near the ellipsoid, 𝑘𝑔 increases to values larger than 1 along the semi-major axis direction, indicating increased gravitational forces. Along the semi-minor axis direction, we see that 𝑘𝑔 <1. Figure 1: Calculated gravitational forces for two different mass distributions References [1] Hartle, J. B. Gravity: an introduction to Einstein's general relativity. (Addison-Wesley, 2003). [2] Binney, J. & Tremaine, S. Galactic dynamics. (Princeton University Press, 1987). . Path integral over causal spacetimes – a non-perturbative approach E M Howard1 1Macquarie University, Sydney, NSW, 2000, Australia We attempt to describe the causal structure of quantum spacetime as a path integral over geometries in a nonperturbative approach of quantum gravity theory. As we know, gravity can’t be described as a renormalizable quantum field theory within a four dimensional spacetime. A perturbative expansion around a fixed background geometry leads to a non-renormalizable theory. The sum-over-histories picture (R. Feynman, J. Hartle) [1] [2] [3] assigns probabilities to different sets of alternatives at definite moments of time, instead of associating quantum states on spacelike surfaces as in Schrodinger-Heisenberg form. In order to keep the “asymptotic safety”, an ultraviolet limit governing the physics at distances shorter than the Planck scale must exist and in its neighbourhood, the co-dimension of the critical surface associated with it should be considered finite. The infrared fixed limit is the ordinary classical general relativity but also should possess a non-trivial ultraviolet cut-off. The complete dynamical nature of geometry, including the diffeomorphism-invariant quantities in the continuum are fully translated into a regularized causal theory. The equivalent notion of observable from SchrodingerHeisenberg formulation is translated into diffeomorphism invariant partitions of spacetime metrics. It is important that the regularization should also restore the apparent broken symmetries of the diffeomorphism invariance in the continuum limit. In this formulation, instead of using alternatives at definite moments of time, we use the more general notion of spacetime alternatives, which is not present in Schrodinger-Heisenberg form. The new generalized spacetime formulation will be completely free from the “problem of time”. We show that causality and the non-local equations of motion can be successfully combined in a picture of a quantum gravity in which there is no well-defined notion of time. Nonlocality and causality seem at first glance incompatible [4]. The primary question is how causality and non-locality coexist in a complete theory of quantum gravity while respecting relativistic causality [5]. The employment of path integrals over spacetime histories should help translating the dynamics associated to unitary evolution into a generalized spacetime form. An accurate sum-over-histories quantum gravity theory should fully predict the probabilities associated with spacetime alternatives while the notion of “measurement” and “observable” should stop playing a fundamental role [6]. The key role in our approach is to separate the notions of causality and causal order between events and the arrow of time. The traditional view of causality is strictly correlated to the unique direction from past to the future, therefore to time’s arrow. All events are described as causally ordered always according to time direction. We suggest that the notion of time is at the origin of the difficulties in formulating a quantum theory of gravity. Based on a clear distinction between the notions of time and causality [7], we search for a new formulation where the quantum laws should be free from any temporal correlations between operators. The causal structure of the spacetime will remain fundamental to a quantum theory but in a more generalized approach of sum-overspacetimes, while “the arrow of time” will be an emergent property from quantum uncertainty but independent from measurement. The longstanding Loschmidt paradox and the origin of irreversible phenomena from reversible timesymmetric physical laws should also find resolution here. The loss of information through quantum entanglement plays the fundamental role here while reaching thermodynamical equilibrium can be understood as a fundamental property of all quantum systems. Entanglement will continue to build up between the state of a quantum system and the state of its external environment, until equilibrium or a state of uniform energy distribution is finally reached. Although there are deep connections between quantum mechanics and irreversibility, there is still an open question if quantum mechanics is strictly required for irreversibility (including why the universe is in a far from equilibrium state). Causality, again, plays a significant role here, as it is intrinsically connected to the non-local character of quantum interactions [8]. A new non-perturbative formulation of quantum gravity can be developed under these new presumptions. As in our approach of quantum gravity, entanglement is the essential ingredient that builds the structure of space-time itself, we suggest that the “arrow of time” emerges from the dynamical nature of spacetime geometry, while transitioning from quantum to classical and requiring a generalized spacetime formulation of quantum mechanics. References [1] R.P. Feynman and A. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York (1965). [2] J.B. Hartle, Unitarity and Causality in Generalized Quantum Mechanics for Non-Chronal Spacetimes, Phys. Rev. D 49, 6543 (1994); quant-ph/9309012. [3] J.B. Hartle, Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime in Gravitation and Quantizations, Les Houches Summer School Proceedings Vol. LVII, Amsterdam (1995); gr-qc/9304006. [4] Y. Aharonov, H. Pendleton, and A. Petersen, Int. J. Theo. Phys. 2 (1969) 213; 3 (1970) 443; Y. Aharonov, in Proc. Int. Symp. Foundations of Quantum Mechanics, Tokyo, 1983, p. 10. [5] S. Popescu and D. Rohrlich, Found. Phys. 24, 379 (1994). [6] N. Yamada and S. Takagi, Prog. Theor. Phys. 87, 77 (1992). [7] E Howard, Causal structure of general relativistic spacetimes, AIP Conference Series, 1246 (2010); grqc/1601.06864. [8] Č. Brukner, Bounding quantum correlations with indefinite causal order, New J. Phys. 17, 073020 (2015). Investigations of the shear-free conjecture for a perfect fluid in general relativity P.A. Huf1 and J. Carminati1 1School of Information Technology, Deakin University, Geelong, Victoria 3216 Australia 1) The conjecture: The shear-free conjecture states that if the shear of a perfect fluid is zero, then either the expansion or rotation of the fluid must be zero. σ=0 =>ωθ=0 It was initially formally stated by Treciokas & Ellis (1971) [1], although there was some related discussion by Gödel (1949) [2]. 6) Role of software in algebraic investigations The algebraic expressions in this conjecture are complex. They can involve many equations including a large number of terms (in tetrad form) or rigid algebraic operations (in covariant formalism). Many research groups employ software programs to assist with calculations. In the current study we have created TensorPack, a new covariant system which assists with abstract index algebraic operations of tensors. The details of this can be seen at [5]. 7) Conclusion The shear-free conjecture, if proven in the general case, will provide additional insight into the Einstein field equations. It can provide a workable comparison between relativistic and Newtonian models. 2) Comparison to the Newtonian model: Importantly this conjecture is in contrast to that predicted by the Newtonian model, where there are known to be shear-free fluids that are both rotating and expanding. The contrasting kinematics of the two models has been discussed in detail by Senovilla et al. [3]. 3) Proofs and sub-cases of the conjecture: In general, the conjecture has not been shown unconditionally, but has been shown for the sub-cases [4]: dust (p=0) (Ellis, 1967) using tetrads; Senovilla et al 2008 using covariant formalism; an alternative covariant proof by Huf & Carminati Magnetic part of the Weyl tensor, H=0 (Collins, 1984) Electric part of the Weyl tensor E=0 (Carminati, 1988) Pure electromagnetic radiation p=(1/3)*mu (Treciokas & Ellis, 1971) P=(-1/3)*mu (Cyganowski & Carminati, 2000) Mixture of matter and radiation: p=(-1/9)*mu (Van den Bergh, 1999) Homogeneous spacetime (King & Ellis, 1973) Acceleration parallel to vorticity (Senovilla et al 2008) For a review see [4]. 4) Hence the motivation for the study involves: The relevance of the conjecture to the FLRW cosmological model Analysis of why there is a difference between the relativistic and Newtonian models 5) The general case is not yet solved, however there are several research groups currently investigating further subcases: The case where acceleration is orthogonal to vorticity; The gamma and affine laws (where density is linear function of energy density). In general, these investigations involve covariant and/or tetrad formalism. Figure 1: The shear-free conjecture References [1] R.E. Treciokas, G.F.R. Ellis, Isotropic Solutions of the Einstein-Boltzmann Equations, Commun. Math. Phys. 23 (1971) 1-22. [2] K. Godel, Rev. An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation. Mod. Phys. 16, (1949) 2361 [3] J.M.M. Senovilla, C.F. Sopuerta, P. Szekeres, P., Theorems on shear-free perfect fluids with their Newtonian analogues, Gen.Rel.Grav, 30 (1998) 389-411. Updated (2008): https://archive.org/details/arxiv-grqc9702035 [4] H. R Karimian. Contributions to the study of shear-free and of purely radiative perfect fluids in general relativity. PhD thesis (2012) [5] P.A.Huf, J.Carminati. TensorPack: a Maple-based software package for the manipulation of algebraic expressions of tensors in general relativity. J.Phys.Conf.Ser. (2015) 633 Making Sense of Gravity Peter R. Lamb1 1Institute for Frontier Materials, Deakin University Waurn Ponds, VIC 3216 Australia A fully relative theory of gravity (FRT) is outlined that reproduces all the standard, observationally confirmed, predictions of general relativity theory (GRT). However, it avoids the need to hypothesise dark energy, dark matter and cosmic inflation; explains the apparent absence of antimatter; and is consistent with quantum mechanics and the Standard Model of particle physics. Gravity still arises from a distortion of space-time by the energy stored in matter as mass. However, the distortion is a simple expansion/contraction of space proportional to the product of the speed of light and the time interval, and not a hidden curvature in the underlying geometry. The result is that magnitudes of physical laws have to be normalised by the stored energy density but space is always flat. The theory and observational consequences are set out more fully elsewhere but give mathematically equivalent results when examining small changes in a large background [1]. One consequence is that the energy stored by particles, oscillating states, decreases as the surrounding (background) energy density increases. This leads to the beautiful understanding that when an object falls in a gravitational field some of its stored energy (mass) is converted into the kinetic energy of motion. In contrast, GRT hypothesises that the mass stays constant but the kinetic energy comes from the surrounding field which is then stronger, because all energy contributes to the field. Under the rubber sheet analogy, in which masses distort space-time leading to the apparent bending of light, GRT has it that a surrounding uniform distribution of matter has no effect on the distortion. It makes more sense to have a central mass producing less distortion when there is more surrounding matter. This is what is observed with a real rubber sheet and, moreover, the speed of a wave propagating on the sheet increases. FRT similarly has the wave speed c increasing, but the energy stored as mass obeying m E / c 2 , with mass reducing as c increases. Under GRT, the speed of light is constant and distortions from matter in opposite directions in space cancel. This cannot happen unless an expansion is matched by a contraction, which is denied by symmetry. Under FRT, the strength of gravitational interactions, length intervals, the speed of light and the clock-rate are all dependent on the background stored energy density. Thus, going back in time, when the density of matter was larger because the universe had expanded less, the clock-rate will have been slower and the speed of light higher. The amount is just right to explain the apparent faintness of distant supernovae without the need to postulate dark energy (Figure 1). It also allows now distant parts of the universe to have been previously in equilibrium without hypothesising (faster than the speed of light) inflation. The rotation curves of spiral galaxies are also explained without the need for dark matter if the background stored energy density tends to zero away from the centre of spiral galaxies. This is possible if there is an approximately uniform distribution of antimatter galaxies and is allowed because FRT has it that matter and antimatter, but not light, would be deflected from such boundaries so that no annihilation signal would be seen. It would be desirable to confirm that the gravitational lensing of like-matter galaxy clusters can be fitted without the need for dark matter. The equality of antimatter allows the underlying physical laws to be symmetric with the apparent asymmetry arising from the local excess of matter. There are many other implications of FRT including that the event horizons and singularities of dense concentrations of matter (supposed black holes) cannot exist. This should already have been appreciated, as it has been pointed out that the idea that a photon loses energy in escaping a gravitational field is mistaken [2-4]. The energy is unchanged, it is the space-time of massive objects that is altered, and so light cannot be trapped by gravity. Another implication is that clock-rate must be increasing as the universe expands and the amount accounts for most of the observed Pioneer anomaly. The implications for particle physics are profound and appear to fully support the Standard Model with three flavour families and massless neutrinos that can nevertheless oscillate, while yielding a revised understanding of the Higgs mechanism and a prediction that the Higgs boson mass should be mW (mZ / 2) = 125.979±0.024 GeV/c2 [5], cf. 125.09±0.24 GeV/c2 measured [6]. Figure 1: Type 1a supernovae data [5] for luminosity distance versus raw (Z) and corrected distance (Z(1+Z/2)). References [1] P. R. Lamb, A Fully Relative Theory of Gravitation, version dated July 4, 2016: http://dro.deakin.edu.au/view/DU:30054938. [2] T.-P. Cheng, Relativity, Gravitation and Cosmology: A Basic Introduction (OUP, 2009), 2nd ed. pp.77-111. [3] L. B. Okun, K. G. Selivanov and V. L. Telegdi, Am. J. Phys. 68, 115 (2000). [4] J. Schwinger, Einstein's Legacy: The Unity of Space and Time (Scientific American, New York, 1986), p. 142. [5] J. Beringer et al. Phys. Rev. D 86, 1 (2012). [6] G. Aad et al. Phys. Rev. Lett. 114, 191803 (2015). [7] N. Suzuki et al., Astrophys. J. 746, 85 (2012). Hovering vs Falling: Perspectives of black holes Colin MacLaurin1 1 School of Mathematics and Physics, The University of Queensland, Brisbane, Qld, Australia The properties of a black hole are typically interpreted using Schwarzschild coordinates. In many ways, these correspond to the measurements of observers hovering at fixed locations. While this is a natural choice to make, it is certainly not the only possibility. The measurements of observers freefalling radially offer a contrasting perspective, and serve as a reminder that in relativity space and time depend on the motion of the observer. −1/2 dr is For instance the textbook radial distance 1− 2M r 1 what hovering observers measure, but this generalises to |e| dr for observers moving with arbitrary energy per mass e. As another example, the space part of spacetime may be represented by a curved funnel known as “Flamm’s paraboloid”. This is also based on the hovering perspective, however the falling observers measure space to be cone-shaped! It is commonly stated that a rock falling into a black hole will take a finite time as measured on its own watch, but that an observer far away would determine an infinite time. However simultaneity is relative, and this is based on a hovering perspective. Under the freefalling observers’ definition of simultaneity, the rock and the distant observer record similar times for the passage. Another popular description is that “time and space swap roles inside the event horizon”. However there are popular coordinate systems for falling observers for which this is not the case. In conclusion, the contrasting perspectives of hovering and falling observers clarify relativistic concepts and yield a broader understanding of black holes. Static vs Falling: M 2.3 r= Time slicings of Schwarzschild black holes Colin MacLaurin www.ColinsCosmos.com Introduction Length-contraction (and expansion) Popular descriptions of black holes often treat the Schwarzschild coordinate time slicing as absolute, speaking of "the" distance, "the" space etc, with only limited qualification of which observers are making these measurements. According to Eisenstaedt such a "neoNewtonian" interpretation lasted until the 1960s, when "black holes" replaced "frozen stars" as the model of collapse. However vestiges of misinterpretation remain. We contrast the perspectives of static and falling observers to emphasise the "relativity" of black holes. A faller and static observer have relative 3-velocity given by the Lorentz factor: The radial lengths obtained previously are factors of and relative to the static distance: M 2.3 r= Observer families and coordinates M 2.3 r= Suppose spacetime is filled with observers, all freefalling radially inward with the same "energy per unit mass" e. All descriptions are a conglomeration of local measurements. M 2.2 r= 2.2M r= e is invariant along a geodesic. Taylor & Wheeler use the metaphors rain/hail/drip, however the case is often forgotten, which I dub "mist": 1M r=2. M r= Choosing adapted coordinate systems is insightful: Generalised Gullstrand-Painleve coordinates: 2.1 Faller perspective: both the static observers and the distance between them are increasingly lengthcontracted as r decreases. Static perspective: both the fallers and the distance between them are increasingly length-contracted. Generalised Lemaitre coordinates: "Space" part of spacetime Use Schwarzschild coordinates for e=0 observers, since these are comoving (constant t). Radial distance The textbook radial "proper distance" is what static observers measure: We can depict the curvature of space by a 2D surface embedded in Euclidean same curvature. Take a constant "time" slice and equatorial slice cylindrical coordinates the embedded surface z=z(r) has metric with the . In Comparing, we obtain: But for observers with arbitrary radial motion, this generalises to: and References [1] R. Gautreau & R. Hoffmann (1978) The slicing is not by Schwarzschild time, but adapted to the fallers. Also different observers determine a different radial direction: though the above are both made by a falling observer, they are measured in the faller and static radial 4-directions respectively. Four equivalent approaches: - adapted coordinates: set - spatial projector: To static observers, space is a funnel, "Flamm's paraboloid". - orthonormal tetrad frames: - radar metric: To the falling family, space is a cone for |e|<1. For |e|=1 it is a flat plane, and for |e|>1 it cannot be depicted by this method. Time and space inside the event horizon The Schwarzschild r-coordinate becomes timelike inside the event horizon. However this must be defined by the hypersurface r=const, and not by the coordinate vector which depends also on the other coordinates bundled with r: [2] K. Martel & E. Poisson (2001), gr-qc/0001069 Coordinates Inner product ∂r ·∂r = grr 1− 2M r Schwarzschild [3] T. Finch (2015), gr-qc/1211.4337 The traditional perspective of infall is what static observers measure, at least somewhat. The fallers' own perspective ("measurement") of their infall is more natural. 3-Volume The spatial volume inside the event horizon is relative to the motion of the observers measuring it. Since the angular part of the metric is the Euclidean 2-sphere, and the radial distance is proportional to r, the volume is proportional to the familiar Euclidean volume as below. More formally, the volume element is: generalised Gullstrand-Painlevé generalised Lemaˆ ıtre Eddington-Finkelstein (null version) Eddington-Finkelstein (timelikeversion) −1 1 e2 1 2 (e −1+ 2M r ) e2 Interpretation spacelikefor r > 2M timelikefor r < 2M spacelike spacelike 0 null 1+ 2M r spacelike Though the coordinates r are identical (as maps ), the coordinate vectors are not. In contrast, the surfaces r=const are independent of the other coordinates. Hence the r-direction is spacelike everywhere for all observers except e=0, and so our results relating it to length are justified. Clarity is needed with the common interpretations that inside the horizon t and r swap roles, and that r decreases because it is timelike. Conclusions and references Radially moving observers determine interesting slicings of Schwarzschild spacetime. Generalised Gullstrand-Painleve and Lemaitre coordinates are insightful about black holes. which integrates to: Finch shows this for e>0. Note raindrops (e=1) measure flat 3-space (Lemaitre 1933), as do "mist rain" (e=-1) observers, hence both measure the Euclidean volume. - MacLaurin, C.; Davis, T.; Lewis, G., in preparation Gautreau & Hoffmann (1978) Taylor & Wheeler, Exploring Black Holes (2000) Martel & Poisson (2001), gr-qc/0001069 Finch (2015), gr-qc/1211.4337v2 Figure 1: Existing version of poster Dynamical angled brane Kei-ichi Maeda1 and Kunihito Uzawa2 1 Department of Physics, Waseda University, Okubo 3-4-1, Shinjuku Tokyo 169-8555, Japan Department of Physics, School of Science and Technology, Kwansei Gakuin University, Sanda, Hyogo 669-1337, Japan 2 We present the dynamical D-brane solutions describing any number of D-branes whose relative orientations are given by certain SU(2) rotations. These are the generalization of the static angled D-brane solutions. We study the collision of dynamical D3-brane with angles in type II string theory, and show that the particular orientation of the smeared D3-brane configuration can provide an example of colliding branes if they have the same charges. Otherwise a singularity appears before D3-branes collide. 1) What is angled D-brane? During the past two decades, understanding of non-perturbative aspects of string theory has advanced constantly. The development of these string theories has brought with it the realization that extended objects such as Dirichlet membranes (D-branes) beyond simply strings play a crucial role. Another significant fact is that more general D-brane solutions arise if the gravity is coupled not only to single gauge field but to several combinations of scalars and forms as intersecting brane solutions in the string theory [1]. The intersections presented are actually orthogonal in the sense that each D-brane lies along some definite directions. It is however possible to show that some configurations of several D-branes intersecting at angles are still supersymmetric. Preserving supersymmetry in such multiple D-brane configurations requires that the angles are restricted to lie in an SU(N) subgroup of rotations [2]. These static configurations may be useful in trying to understand the microscopic counting of states of four-dimensional black holes in string theories. 2) Motivation: “Why are angled D-branes studied?” Although the time-dependent D-brane solutions in string theory were introduced in [1, 3] and have been widely used ever since, some aspects of the physical properties such as dynamical D-brane oriented at angles and the corresponding background field configurations remain largely unexplored. Our motivation for the present work is to improve this situation. The static angled D-brane solutions was discovered by [2] following the recognition of the several role of D-brane configurations in string theory. The classical solution on ten-dimensional spacetime that should be obtained to introduce oriented at angles in string theories were studied from several points of view. They have discussed the link between the supersymmetric configurations, intersection of brane and the rotation angles. The article [4] gives a thorough review of much of what was known in the late 1990's. These results are more transparent if the dynamical D-brane solution in string theory is discussed in terms of supergravity theory, aiming to reduce everything to ordinary higher-dimensional general relativity. In our poster, we construct new solutions with nontrivial angles in string theory and study the dynamical behaviour that one would expect of a string theory with the time-dependent fields and D-branes. 3) Our methods and results We discuss the dynamical D-brane solution which shows several D-branes oriented at angles with respect to one another. Since the corresponding background field configurations remain largely unclear, we present one such class of solutions in the time-dependent D-brane background. The dynamical solution which we construct in this poster describes any number of D-brane whose relative orientations are given by certain SU(2) rotations [5]. These are functions of time that becomes static near D-branes with the simplest possible dependence on the warp factor. In the far region from angled D-brane in the ten-dimensional background, the solutions give purely contracting or expanding anisotropic universe. We also provide more details about the collision of two D3-branes (three-dimensional Dirichlet membranes) in the presence of angles. The two D3-branes approach at an angle in the direction of spatial part of world volume coordinates. We have studied the dynamics of D3-branes which have been smeared along the transverse space to D3-branes. If two D3-brane charges are different from each other, the distance between two D3-branes is still finite when a singularity appears. Thus, we cannot describe the collision of two D3-branes in terms of the solution. On the other hand, there exists a complete collision where the orientations of configurations between two smeared D3-branes with same charges are either 0 or pi. This result may be related to supersymmetry, which may be broken for non-parallel branes. 4) Outlook for the future Although the examples presented in our poster cannot provide a realistic cosmological model, the solution may be utilized to construct a cosmological solution just by introduction of a test brane universe in higher-dimensions. We may also construct new type of time-dependent black hole solution with non-trivial angles by setting up more complicated D-brane configuration. Those subjects are left for a future works. References [1] K. Maeda, N. Ohta, K. Uzawa, JHEP 0906 (2009) 051 [2] J. C. Breckenridge, G. Michaud, R. C. Myers, Phys. Rev. D 56 (1997) 5172 [3] G. W. Gibbons, H. Lu, C. N. Pope, Phys. Rev. Lett. 94 (2005) 131602 [4] D. Youm, Phys. Rept.316 (1999) 1 [5] K. Maeda, K. Uzawa, arXiv:1603.01948