M. Dehghani

Conformally invariant 'massless' spin-2 field in the de Sitter universe

A massless spin-2 field equation in de Sitter space, which is invariant under the conformal transformation, has been obtained. The framework utilized is the symmetric rank-2 tensor field of the conformal group. Our method is based on the group theoretical approach and six-cone formalism, initially introduced by Dirac. Diracs six-cone is used to obtain conformally invariant equations on de Sitter space. The solution of the physical sector of massless spin-2 field (linear gravity) in de Sitter ambient space is written as a product of a generalized polarization tensor and a massless minimally coupled scalar field. Similar to the minimally coupled scalar field, for quantization of this sector, the Krein space quantization is utilized. We have calculated the physical part of the linear graviton two-point function. This two-point function is de Sitter invariant and free of pathological large-distance behavior.

GUP and higher dimensional Reissner-Nordström black hole radiation

Based on the generalized uncertainty principle (GUP), in which the quantum gravitational effects are taken in to account, the corrected Beckenstein-Hawking entropy of the higher dimensional Reissner-Nordstrom black hole, up to the square order of Planck length, is calculated. Using the corrected entropy, the black hole radiation probability is calculated in the tunneling formalism, which is corrected up to the same order of the Planck length and shows a more probable quantum tunneling.

COVARIANT TWO-POINT FUNCTION FOR MASSLESS SPIN-2 FIELD IN DE SITTER SPACE

The linearized gravitational field equation in de Sitter (dS) four-dimensional space is gauge invariant under some special gauge transformations. It is also gauge invariant in ambient space notations in which the field equation is written in terms of the Casimir operators of dS group. In this paper the field equation is solved in terms of a gauge-fixed value (i.e. in the minimal case). It is shown that the solution can be written as the multiplication of a generalized symmetric rank-2 polarization tensor and a massless minimally coupled scalar field in ambient space notations. The two-point function is calculated in ambient space notations, which is dS-invariant and free of any divergences. This two-point function has been expressed in terms of dS intrinsic coordinates, from its ambient space counterpart, which is clearly dS-invariant and free of any divergences again.

Group theoretical interpretation of the modified gravity in de Sitter space

A bstractA framework has been presented for theoretical interpretation of various modified gravitational models which is based on the group theoretical approach and unitary irreducible representations (UIR’s) of de Sitter (dS) group. In order to illustrate the application of the proposed method, a model of modified gravity has been investigated. The background field method has been utilized and the linearized modified gravitational field equation has been obtained in the 4-dimensional dS space-time as the background. The field equation has been written as the eigne-value equation of the Casimir operators of dS space using the flat 5-dimensional ambient space notations. The Minkowskian correspondence of the theory has been obtained by taking the zero curvature limit. It has been shown that under some simple conditions, the linearized modified field equation transforms according to two of the UIR’s of dS group labeled by Π2,1± and Π2,2± in the discrete series. It means that the proposed modified gravitational theory can be a suitable one to describe the quantum gravitational effects in its linear approximation on dS space. The field equation has been solved and the solution has been written as the multiplication of a symmetric rank-2 polarization tensor and a massless scalar field using the ambient space notations. Also the two-point function has been calculated in the ambient space formalism. It is dS invariant and free of any theoretical problems.

EVALUATION OF THE GRAVITON TWO-POINT FUNCTION IN DE SITTER SPACE

After a brief review of the linearized gravity in de Sitter (dS) four-dimensional space and ambient flat five-dimensional notations, the linearized field equation is written in terms of the Casimir operators of dS group. It is shown that the field equation is gauge invariant under some special gauge transformations. Because of this gauge freedom, a gauge-fixing parameter c is inserted in the field equation. It is shown that the solution to the field equation can be written as the multiplication of a generalized symmetric rank-2 polarization tensor and a massless minimally coupled scalar field in ambient space notations. The graviton two-point function has been thoroughly calculated, which is dS-invariant and free of any divergences. This two-point function has been expressed in terms of the intrinsic dS coordinates, from its ambient space counterpart, which is clearly dS-invariant and free of any divergences again.

Planck-Scale Corrections to the Cardy–Verlinde Formula in SAdS Black Hole

Possible corrections to the thermodynamic quantities of a 4D Schwarzschild–anti–de Sitter (SAdS) black hole are investigated by considering the generalized uncertainty principle (GUP) and the modified dispersion relation (MDR) separately. The quantum gravitational corrections to the Hawking temperature, energy and entropy of the black hole are calculated based on both the GUP and the MDR analysis. The explicit form of the corrections is worked out up to the sixth power of the Planck length. The quantum-corrected thermodynamic quantities due to GUP and MDR are used separately to obtain the quantum-gravitational corrections to the Cardy–Verlinde (C–V) formula. It is found that the C–V formula receives some new corrections in either of approaches. Through comparison of the corrections obtained from GUP and MDR approaches, it is shown that the results of these two alternative approaches should be identical if one uses the suitable expansion coefficients. Finally, the renormalized form of the C–V formula is introduced by redefining the Virasoro operator and the central charge within both the GUP and the MDR.