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Register a new userDirac Relaxation of the Israel Junction Conditions: Unified Randall-Sundrum Brane Theory
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Following Diracs brane variation prescription, the brane must not be deformed during the variation process, or else the linearity of the variation may be lost. Alternatively, the variation of the brane is done, in a special Dirac frame, by varying the bulk coordinate system itself. Imposing appropriate Dirac style boundary conditions on the constrained sandwiched gravitational action, we show how Israel junction conditions get relaxed, but remarkably, all solutions of the original Israel equations are still respected. The Israel junction conditions are traded, in the $Z_2$-symmetric case, for a generalized Regge-Teitelboim type equation (plus a local conservation law), and in the generic $Z_2$-asymmetric case, for a pair of coupled Regge-Teitelboim equations. The Randall-Sundrum model and its derivatives, such as the Dvali-Gabadadze-Porrati and the Collins-Holdom models, get generalized accordingly. Furthermore, Randall-Sundrum and Regge-Teitelboim brane theories appear now to be two different faces of the one and the same unified brane theory. Within the framework of unified brane cosmology, we examine the dark matter/energy interpretation of the effective energy/momentum deviations from General Relativity.
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The presence of tidal charge and a cosmological constant has considerable consequences on the spacetime geometry and its study is much important from the observational point of view. Henceforth, we investigate their effects on particle dynamics and the shadow cast by a Randall-Sundrum braneworld black hole with a cosmological constant. On studying the circular geodesics of timelike particles, we have acquired the expressions of energy, angular momentum and effective potential. We noted that the negative values of tidal charge and cosmological constant decreases the energy of particles. In addition, the negative value of cosmological constant leads us to the stable circular orbits, whereas its positive value destabilizes the circular orbits. Our exploration shows that the cosmological constant diminishes the radius of the black hole shadow. In response to the dragging effect, black hole rotation elongates its shadow toward the rotational axis. Besides, black hole spin and positive charge distort shadow and its distortion become maximum as far as the black hole rotates faster. We also discussed the energy emission rate by considering different cases and compared our result with the standard Kerr black hole.
We study the effect of the inclusion of bulk brane viscosity on brane world (BW) cosmology in the framework of the Eckarts theory, we focus in the Randall-Sundrum model with negative tension on the brane.
Adopting Diracs brane variation prescription, the energy-momentum tensor of a brane gets supplemented by a geometrical (embedding originated) dark component. While the masslessness of the graviton is preserved, and the Newton force law is recovered, the corresponding Newton constant is necessarily lower than the one which governs FRW cosmology. This has the potential to puzzle out cosmological dark matter, a subsequent conjecture concerning galactic dark matter follows.
In this paper we study the Statefinder and $Om(x)$ diagnoses of an exact solution of a unified dissipative dark matter model in the framework the Israel-Stewart theory and its non linear extension, considering the condition of positive entropy production. The implementation of two diagnoses in the pair of solutions reveal that both solutions can emulate the $Lambda$CDM model at some stage of the cosmic evolution and behave as quintessence dark energy. The stability of both solutions is discussed from the point of view of the Liapunovs method, showing that they are asymptotic stable. Additionally we show that the solutions are also stable under small perturbations. A simple analysis of the solutions with the use of observational data suggests that the non linear regime could lead to a inconsistencies-free scenario, i.e., in agreement with the bounds obtained from the perturbative analysis for the velocity of bulk viscous perturbations.
We analyze junction conditions at a null or non-null hypersurface $Sigma$ in a large class of scalar-tensor theories in arbitrary $n(ge 3)$ dimensions. After showing that the metric and a scalar field must be continuous at $Sigma$ as the first junction conditions, we derive the second junctions conditions from the Einstein equations and the equation of motion for the scalar field. Subsequently, we study $C^1$ regular matching conditions as well as vacuum conditions at $Sigma$ both in the Jordan and Einstein frames. Our result suggests that the following configurations may be possible; (i) a vacuum thin-shell at null $Sigma$ in the Einstein frame, (ii) a vacuum thin-shell at null and non-null $Sigma$ in the Jordan frame, and (iii) a non-vacuum $C^1$ regular matching at null $Sigma$ in the Jordan frame. Lastly, we clarify the relations between the conditions for $C^1$ regularity and also for vacuum $Sigma$ in the Jordan and Einstein frames.
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