Bhagya. R

We investigate the modification of the Stefan-Boltzmann law in the space-time whose geometry is energy-dependent. From the energy-momentum tensor of the electromagnetic field in rainbow space-time, we obtain the energy density of the isotropic radiation, valid up to the first order in the rainbow parameters. Using this in the first law of thermodynamics, we find the change in entropy of the radiation, and from this, the Stefan-Boltzmann relation is derived. We show that for two choices of the rainbow functions, the temperature dependence of the energy of the radiation is different from the $T^4$ law. We have also derived the corrections to Wien's displacement law in the rainbow space-time.

In this paper, we derive maximal acceleration of a massive particle in Rainbow gravity. Using eight-dimensional phase-space metric compatible with Rainbow gravity, we obtain the maximal acceleration, valid up to first order in the Rainbow gravity parameter $η$. Using the positivity condition on maximal acceleration, we find the upper bound on the Rainbow gravity parameter is of the order of $~10^{22}$ for positron and $10^{-44}$ for a black hole. After obtaining the expression for maximal acceleration for different choices of Rainbow functions, we derive corresponding modifications to Unruh temperature. Comparing with the observational value of the Unruh temperature, we find the upper bound on $η$ as $~10^{32}$ for positron radiation. %and of the order of $10^{-100}$ for radiation from a black hole. We then derive geodesic equations for different choices of Rainbow functions and also obtain Newtonian limit of these geodesic equations. We find that the changes in the value of maximum acceleration, maximum temperature and Newtonian force equation are dependent on the choices of Rainbow functions.

We study a model of the neutron star in $κ$-deformed space-time in the presence of the cosmological constant ($Λ$). The Einstein tensor and the energy-momentum tensor are generalized to $κ$-deformed space-time and we construct the field equations with the cosmological constant. Considering the interior of the star to be a perfect fluid as in the commutative case, we find the Tolman-Oppenheimer-Volkoff equations with the inclusion of the cosmological constant in $κ$-deformed space-time. The behavior of the maximum allowed mass of the star and its radius are studied with the variation in the cosmological constant as well as the deformation parameter. We see that the non-commutativity enhances the mass of the star and its maximum mass increases with a decrease in the cosmological constant. The maximum mass varies from $3.44M_{\odot}$ to $3.68M_{\odot}$ as $Λ$ varies from $10^{-10}m^{-2}$ to $10^{-15}m^{-2}$. We also obtain the compactness factor and surface redshift of the star. We observe that the compactness of the star increases as the cosmological constant decreases, whereas the surface redshift of the star decreases with a decrease in the cosmological constant. The compactness factor and surface redshift corresponding to the maximum mass of the neutron star remains almost constant as $Λ$ decreases.

We construct and analyze a model of the neutron star in the k deformed space-time. This is done by first deriving the k deformed generalization of the Einstein tensor, starting from the non-commutative generalization of the metric tensor. By generalizing the energy momentum tensor to the non-commutative space-time and exploiting the k deformed dispersion relation, we then set up Einstein's field equations in the kdeformed space time. As we adopt a realization of the non commutative coordinates in terms of the commutative coordinates and their derivatives, our model is constructed in terms of commutative variables. Using this, we derive the kdeformed generalization of the Tolman Oppenheimer Volkoff equation. Now, by treating the interior of the star to be a perfect fluid as in the commutative space-time, we investigate the modification of the neutron star's mass due to non commutativity of the space time, valid up to first order in the deformation parameter. We show that the non-commutativity of the space time enhances the mass limit of the neutron star. We show that the radius and maximum mass of the neutron star depend on the deformation parameter. Further, our study shows that the mass increases as the radius increases for fixed values of the deformation parameter. We show that maximum mass and radius increase as the deformation parameter increases. We find that the mass varies from 0.26Ms to 3.68Ms as radius changes from 8.45km to 18.66km. Using the recent observational limits on the upper bound of the mass of a neutron star, we find the deformation parameter is approximately $10^{-44}m$. We also show that the compactness and surface redshift of the neutron star increase with its mass.

We construct and analyze a model of a neutron star in a $\kappa$-deformed space-time. This is conducted by first deriving the $\kappa$-deformed generalization of the Einstein tensor, starting from the non-commutative generalization of the metric tensor. By generalizing the energy-momentum tensor to the non-commutative space-time and exploiting the $\kappa$-deformed dispersion relation, we then set up Einstein’s field equations in the $\kappa$-deformed space-time. As we adopt a realization of the non-commutative coordinates in terms of the commutative coordinates and their derivatives, our model is constructed in terms of commutative variables. Using this, we derive the $\kappa$-deformed generalization of the Tolman–Oppenheimer–Volkoff equation. Now, by treating the interior of the star as a perfect fluid as in the commutative space-time, we investigate the modification of the neutron star’s mass due to the non-commutativity of space-time, valid up to first order in the deformation parameter. We show that the non-commutativity of space-time enhances the mass limit of the neutron star. We show that the radius and maximum mass of the neutron star depend on the deformation parameter. Further, our study shows that the mass increases as the radius increases for fixed values of the deformation parameter. We show that maximum mass and radius increase as the deformation parameter increases. We find that the mass varies from $0.26M_{\odot }$ to $3.68M_{\odot }$ as the radius changes from $8.45$ km to $18.66$ km. Using the recent observational limits on the upper bound of the mass of a neutron star, we find the deformation parameter to be $\left|a\right|\sim {10}^{-44}$ m. We also show that the compactness and surface redshift of the neutron star increase with its mass.