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Register a new userRandall-Sundrum model with $lambda<0$ and bulk brane viscosity
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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.
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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.
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 derive the low-energy effective theory of gravity for a generalized Randall-Sundrum scenario, allowing for a third self-gravitating brane to live in the 5D bulk spacetime. At zero order the 5D spacetime is composed of two slices of anti-de Sitter spacetime, each with a different curvature scale, and the 5D Weyl tensor vanishes. Two boundary branes are at the fixed points of the orbifold whereas the third brane is free to move in the bulk. At first order, the third brane breaks the otherwise continuous evolution of the projection of the Weyl tensor normal to the branes. We derive a junction condition for the projected Weyl tensor across the bulk brane, and combining this constraint with the junction condition for the extrinsic curvature tensor, allows us to derive the first-order field equations on the middle brane. The effective theory is a generalized Brans-Dicke theory with two scalar fields. This is conformally equivalent to Einstein gravity and two scalar fields, minimally coupled to the geometry, but nonminimally coupled to matter on the three branes.
We present a Randall-Sundrum toy model with an added scalar singlet that couples only to KK fermions in the bulk. Such a scalar would nontrivially affect radion phenomenology. In addition, we examine the radion phenomenology in light of the new scalar and show how this scalar could present another probe to search for the radion.
A generalization from the usual $5$-dimensional two-brane Randall-Sundrum (RS) model to a $6$-dimensional multi-brane RS model is presented. The extra dimensions are extended from one to two; correspondingly the single-variable warp function is generalized to be a double-variable function, to represent the two extra dimensions. In the analysis of the Einstein equation we have two remarkable discoveries. One is that, when branes are absent, the cosmological parameter distributed in the two extra dimensions acts as a function describing a family of circles. These circles are not artificially added ones but stem from the equations of motion, while their radii are inversely proportional to the square root of the cosmological parameter. The other discovery is that, on any circle, there symmetrically distribute four branes. Their tensions, $V_1 sim V_4$, satisfy a particular relationship $V_1=V_3=-V_2=-V_4=3M^4$, where $M$ is the $6$-dimensional fundamental scale of the RS model.
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