| 1. |
- Hassan, Sayed Fawad, et al.
(författare)
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On the local structure of spacetime in ghost-free bimetric theory and massive gravity
- 2018
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :5
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Tidskriftsartikel (refereegranskat)abstract
- The ghost-free bimetric theory describes interactions of gravity with another spin-2 field in terms of two Lorentzian metrics. However, if the two metrics do not admit compatible notions of space and time, the formulation of the initial value problem becomes problematic. Furthermore, the interaction potential is given in terms of the square root of a matrix which is in general nonunique and possibly nonreal. In this paper we show that both these issues are evaded by requiring reality and general covariance of the equations. First we prove that the reality of the square root matrix leads to a classification of the allowed metrics in terms of the intersections of their null cones. Then, the requirement of general covariance further restricts the allowed metrics to geometries that admit compatible notions of space and time. It also selects a unique definition of the square root matrix. The restrictions are compatible with the equations of motion. These results ensure that the ghost-free bimetric theory can be defined unambiguously and that the two metrics always admit compatible 3+1 decompositions, at least locally. In particular, these considerations rule out certain solutions of massive gravity with locally Closed Causal Curves, which have been used to argue that the theory is acausal.
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| 2. |
- Högås, Marcus, et al.
(författare)
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Generalized Vaidya solutions in bimetric gravity
- 2020
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 37:14
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Tidskriftsartikel (refereegranskat)abstract
- In general relativity, the endpoint of spherically symmetric gravitational collapse is a Schwarzschild-[(A)dS] black hole. In bimetric gravity, it has been speculated that a static end state must also be Schwarzschild-[(A)dS]. To this end, we present a set of exact solutions, including collapsing massless dust particles. For these, the speculation is confirmed.
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| 3. |
- Kocic, Mikica, et al.
(författare)
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Algebraic properties of Einstein solutions in ghost-free bimetric theory
- 2019
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 60:10
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Tidskriftsartikel (refereegranskat)abstract
- A fact is that an Einstein solution in one sector in ghost-free bimetric theory implies an Einstein solution in the other sector. Earlier studies have also shown that some classes of bimetric models necessitate proportional solutions between the sectors. Here, we consider a general setup of the parameters in the theory as well as the general algebraic form of the potential. We show that, if one sector has an Einstein solution, the solutions are either proportional or block proportional with at most two different eigenvalues in the square root governing metric interactions.
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| 4. |
- Kocic, Mikica
(författare)
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Causal propagation of constraints in bimetric relativity in standard 3+1 form
- 2019
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :10
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Tidskriftsartikel (refereegranskat)abstract
- The goal of this work was to investigate the propagation of the constraints in the ghost-free bimetric theory where the evolution equations are in standard 3+1 form. It is established that the constraints evolve according to a first-order symmetric hyperbolic system whose characteristic cone consists of the null cones of the two metrics. Consequently, the constraint evolution equations are well-posed, and the constraints stably propagate.
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| 5. |
- Kocic, Mikica
(författare)
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Geometric mean of bimetric spacetimes
- 2021
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 38:7
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Tidskriftsartikel (refereegranskat)abstract
- We use the geometric mean to parametrize metrics in the Hassan-Rosen ghost-free bimetric theory and pose the initial-value problem. The geometric mean of two positive definite symmetric matrices is a well-established mathematical notion which can be under certain conditions extended to quadratic forms having the Lorentzian signature, say metrics g and f. In such a case, the null cone of the geometric mean metric h is in the middle of the null cones of g and f appearing as a geometric average of a bimetric spacetime. The parametrization based on h ensures the reality of the square root in the ghost-free bimetric interaction potential. Subsequently, we derive the standard n + 1 decomposition in a frame adapted to the geometric mean and state the initial-value problem, that is, the evolution equations, the constraints, and the preservation of the constraints equation.
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| 6. |
- Kocic, Mikica
(författare)
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Geometry of interactions in ghost-free bimetric theory
- 2017
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The ghost-free bimetric theory is an extension to general relativity where two metric tensors are used instead of one. A priori, the two metrics may not have compatible notions of space and time, which makes the formulation of the initial-value problem problematic. Moreover, the metrics are coupled through a specific ghost-free interaction term that is nonunique and possibly nonreal. We prove that the reality of the bimetric potential leads to a classification of the allowed configurations of the two metrics in terms of the intersections of their null cones. Then, the equations of motion and general covariance are enough to restrict down the allowed configurations to metrics that admit compatible notions of space and time, and furthermore, lead to a unique definition of the potential. This ensures that the ghost-free bimetric theory can be defined unambiguously. In addition, we apply the results on spherically symmetric spacetimes. First, we explore the behavior of the black hole solutions both at the common Killing horizon and at the large radii. The study leads to a new classification for black holes within the bidiagonal ansatz. Finally, we consider the bimetric field equations in vacuum when the two metrics share a single common null direction. We obtain a class of exact solutions of the generalized Vaidya type parametrized by an arbitrary function. The found solutions are nonstationary and thus nonstatic, which formally disproves an analogous statement to Birkhoff's theorem in the ghost-free bimetric theory.
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| 7. |
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| 8. |
- Kocic, Mikica, et al.
(författare)
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Initial data and first evolutions of dust clouds in bimetric relativity
- 2020
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 37:16
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Tidskriftsartikel (refereegranskat)abstract
- We present a method for solving the constraint equations in the Hassan-Rosen bimetric theory to determine the initial data for the gravitational collapse of spherically symmetric dust. The setup leads to equations similar to those for a polytropic fluid in general relativity, here called Lane-Emden-like equations. Using a numerical code which solves the evolution equations in the standard 3 + 1 form, we also obtain a short-term development of the initial data for these bimetric spherical clouds. The evolution highlights some important features of the bimetric theory such as the interwoven and oscillating null cones representing the essential nonbidiagonality in the dynamics of the two metrics. The simulations are in the strong-field regime and show that, at least at an early stage, if the bimetric initial data are close to those for general relativity, the bimetric evolution stays close to the evolution in general relativity as well, and with no instabilities, albeit with small oscillations in the metric fields. In addition, we determine initial data and first evolution for vacuum bimetric spherically symmetric nonstationary solutions, providing generic counterexamples to a statement analog to Jebsen-Birkhoff theorem in bimetric relativity.
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| 9. |
- Kocic, Mikica, et al.
(författare)
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On Birkhoff's theorem in ghost-free bimetric theory
- 2017
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We consider the Hassan-Rosen bimetric field equations in vacuum when the two metrics share a single common null direction in a spherically symmetric configuration. By solving these equations, we obtain a class of exact solutions of the generalized Vaidya type parametrized by an arbitrary function. Besides not being asymptotically flat, the found solutions are nonstationary admitting only three global spacelike Killing vector fields which are the generators of spatial rotations. Hence, these are spherically symmetric bimetric vacuum solutions with the minimal number of isometries. The absence of staticity formally disproves an analogue statement to Birkhoff's theorem in the ghost-free bimetric theory which would state that a spherically symmetric solution is necessarily static in empty space.
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| 10. |
- Kocic, Mikica, et al.
(författare)
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On the ratio of lapses in bimetric relativity
- 2019
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 36:22
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Tidskriftsartikel (refereegranskat)abstract
- The two lapse functions in the Hassan–Rosen bimetric theory are not independent. Without knowing the relation between them, one cannot evolve the equations in the 3+1 formalism. This work computes the ratio of lapses for the spherically symmetric case, which is a prerequisite for numerical bimetric relativity.
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