http://arxiv.org/abs/0909.4157
Revisiting the semiclassical gravity scenario for gravitational collapse
C. Barcelo, S. Liberati, S. Sonego, M. Visser
(Submitted on 23 Sep 2009)
The existence of extremely dark and compact astronomical bodies is by now a well established observational fact. On the other hand, classical General Relativity predicts the existence of black holes which fit very well with the observations, but do lead to important conceptual problems. In this contribution we ask ourselves the straightforward question: Are the dark and compact objects that we have observational evidence for black holes in the sense of General Relativity? By revising the semiclassical scenario of stellar collapse we find out that as the result of a collapse some alternative objects could be formed which might supplant black holes.
http://arxiv.org/abs/0909.4194
Non-equilibrium Thermodynamics of Spacetime: the Role of Gravitational Dissipation
G. Chirco, S. Liberati
(Submitted on 23 Sep 2009)
In arXiv:gr-qc/9504004 it was shown that the Einstein equation can be derived as a local constitutive equation for an equilibrium spacetime thermodynamics. More recently, in the attempt to extend the same approach to the case of $f(R)$ theories of gravity, it was found that a non-equilibrium setting is indeed required in order to fully describe both this theory as well as classical GR (arXiv:gr-qc/0602001). Here, elaborating on this point, we show that the dissipative character leading to a non-equilibrium spacetime thermodynamics is actually related -- both in GR as well as in $f(R)$ gravity -- to non-local heat fluxes associated with the purely gravitational/internal degrees of freedom of the theory. In particular, in the case of GR we show that the internal entropy production term is identical to the so called tidal heating term of Hartle-Hawking. Similarly, for the case of $f(R)$ gravity, we show that dissipative effects can be associated with the generalization of this term plus a scalar contribution whose presence is clearly justified within the scalar-tensor representation of the theory. Finally, we show that the allowed gravitational degrees of freedom can be fixed by the kinematics of the local spacetime causal structure, through the specific Equivalence Principle formulation. In this sense, the thermodynamical description seems to go beyond Einstein's theory as an intrinsic property of gravitation.
http://arxiv.org/abs/0909.4211
Bianchi I model in terms of non-standard LQC: Classical dynamics
Piotr Dzierzak, Wlodzimierz Piechocki
(Submitted on 23 Sep 2009)
The cosmological singularities of the Bianchi I universe are analyzed in the setting of loop geometry underlying the loop quantum cosmology. We solve the Hamiltonian constraint of the theory and find the Lie algebra of elementary observables. Physical compound observables are defined in terms of elementary ones. Modification of classical theory by holonomy around a loop removes the singularities. However, our model has a free parameter that cannot be determined within our method. Testing the model by the data of observational cosmology may be possible after quantization of our modified classical theory.
http://arxiv.org/abs/0909.4221
Loop Quantum Cosmology and Spin Foams
Abhay Ashtekar, Miguel Campiglia, Adam Henderson
(Submitted on 23 Sep 2009)
Loop quantum cosmology (LQC) is used to provide concrete evidence in support of the general paradigm underlying spin foam models (SFMs). Specifically, it is shown that: i) the physical inner product in the timeless framework equals the transition amplitude in the deparameterized theory; ii) this quantity admits a %convergent vertex expansion a la SFMs in which the $M$-th term refers just to $M$ volume transitions, without any reference to the time at which the transition takes place; iii) the exact physical inner product is obtained by summing over just the discrete geometries; no `continuum limit' is involved; and, iv) the vertex expansion can be interpreted as a perturbative expansion in the spirit of group field theory. This sum over histories reformulation of LQC also addresses certain other issues which are briefly summarized.
http://arxiv.org/abs/0909.4238
2+1 Quantum Gravity with Barbero-Immirzi like parameter on Toric Spatial Foliation
Rudranil Basu, Samir K Paul
(Submitted on 23 Sep 2009)
We consider gravity in 2+1 space-time dimensions, with negative cosmological constant and a `Barbero-Immirzi' (B-I) like parameter, when the space-time topology is of the form $ T^2 \times \mathbbm{R}$. The phase space structure, both in covariant and canonical framework is analyzed. Full quantization of the theory in the 'constrain first' approach reveals a finite dimensional physical Hilbert space. An explicit construction of wave functions is presented. The dimension of the Hilbert space is found to depend on the `Barbero-Immirzi' like parameter in an interesting fashion.
http://arxiv.org/abs/0909.3841
Anisotropic Conformal Infinity
Petr Horava, Charles M. Melby-Thompson
(Submitted on 21 Sep 2009)
We generalize Penrose's notion of conformal infinity of spacetime, to situations with anisotropic scaling. This is relevant not only for Lifgarbagez-type anisotropic gravity models, but also in standard general relativity and string theory, for spacetimes exhibiting a natural asymptotic anisotropy. Examples include the Lifgarbagez and Schrodinger spaces (proposed as AdS/CFT duals of nonrelativistic field theories), warped AdS_3, and the near-horizon extreme Kerr geometry. The anisotropic conformal boundary appears crucial for resolving puzzles of holographic renormalization in such spacetimes.
