Lagrangian Density for Perfect Fluids in General Relativity

1972 ◽  
Vol 13 (10) ◽  
pp. 1451-1453 ◽  
Author(s):  
John R. Ray
Keyword(s):  
General Relativity ◽  
Lagrangian Density ◽  
Perfect Fluids

scholarly journals Stress Energy Tensor Study in Fluid Mechanics

2019 ◽  
Author(s):  
Roman Baudrimont
Keyword(s):  
General Relativity ◽  
Fluid Mechanics ◽  
Space Time ◽  
Newtonian Fluids ◽  
Third Party ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Perfect Fluids ◽  
Stress Energy

This paper is to summarize the involvement of the stress energy tensor in the study of fluid mechanics. In the first part we will see the implication that carries the stress energy tensor in the framework of general relativity. In the second part, we will study the stress energy tensor under the mechanics of perfect fluids, allowing us to lead third party in the case of Newtonian fluids, and in the last part we will see that it is possible to define space-time as a no-Newtonian fluids.

scholarly journals On the Connections between Thermodynamics and General Relativity

2021 ◽  
Author(s):  
◽  
Jessica Santiago Silva
Keyword(s):  
General Relativity ◽  
Hawking Radiation ◽  
Rigid Motion ◽  
Irreversible Thermodynamics ◽  
Temperature Gradients ◽  
Type I ◽  
Killing Vectors ◽  
Proper Distance ◽  
Perfect Fluids ◽  
History Of

<p>In this thesis, the connections between thermodynamics and general relativity are explored. We introduce some of the history of the interaction between these two theories and take some time to individually study important concepts of both of them. Then, we move on to explore the concept of gravitationally induced temperature gradients in equilibrium states, first introduced by Richard Tolman. We explore these Tolman-like temperature gradients, understanding their physical origin and whether they can be generated by other forces or not. We then generalize this concept for fluids following generic four-velocities, which are not necessarily generated by Killing vectors, in general stationary space-times. Some examples are given.  Driven by the interest of understanding and possibly extending the concept of equilibrium for fluids following trajectories which are not generated by Killing vectors, we dedicate ourselves to a more fundamental question: can we still define thermal equilibrium for non-Killing flows? To answer this question we review two of the main theories of relativistic non-perfect fluids: Classical Irreversible Thermodynamics and Extended Irreversible Thermodynamics. We also take a tour through the interesting concept of Born-rigid motion, showing some explicit examples of non-Killing rigid flows for Bianchi Type I space-times. These results are important since they show that the Herglotz–Noether theorem cannot be extended for general curved space-times. We then connect the Born-rigid concept with the results obtained by the relativistic fluid’s equilibrium conditions and show that the exact thermodynamic equilibrium can only be achieved along a Killing flow. We do, however, introduce some interesting possibilities which are allowed for non-Killing flows.  We then launch into black hole thermodynamics, specifically studying the trans-Planckian problem for Hawking radiation. We construct a kinematical model consisting of matching two Vaidya spacetimes along a thin shell and show that, as long as the Hawking radiation is emitted only a few Planck lengths (in proper distance) away from the horizon, the trans-Plackian problem can be avoided.  We conclude with a brief discussion about what was presented and what can be done in the future.</p>

scholarly journals Investigating $f(R)$ gravity and cosmologies

2021 ◽  
Author(s):  
Vaibhav Kalvakota
Keyword(s):  
General Relativity ◽  
Lagrangian Density ◽  
Ricci Scalar ◽  
Metric Tensor ◽  
Extended Theory ◽  
Theories Of Gravity ◽  
Theory Of Gravity ◽  
Hilbert Action ◽  
Geometric Nature

The f (R) theory of gravity is an extended theory of gravity that is based on general relativity in the simplest case of $f(R) = R$. This theory extends such a function of the Ricci scalar into arbitrary functions that are not necessarily linear, i.e. could be of the form $f(R) = \alpha R^{2}$. The action for such a theory would be $S_{EH} = \frac{1}{2k} \int f(R) + L^{m}\; d^{4}x\sqrt{−g}$, where $S_{EH}$ is the Einstein-Hilbert action for our theory, $g$ is the determinant of the metric tensor $g_{\mu \nu}$ and $L^{m}$ is the Lagrangian density for matter. In this paper, we will look at some of the physical implications of such a theory, and the importance of such a theory in cosmology and in understanding the geometric nature of such f (R) theories of gravity.

scholarly journals Stress Energy Tensor Study in Fluid Mechanics

2019 ◽  
Author(s):  
Roman Baudrimont
Keyword(s):  
General Relativity ◽  
Fluid Mechanics ◽  
Space Time ◽  
Newtonian Fluids ◽  
Third Party ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Perfect Fluids ◽  
Stress Energy

This paper is to summarize the involvement of the stress energy tensor in the study of fluid mechanics. In the first part we will see the implication that carries the stress energy tensor in the framework of general relativity. In the second part, we will study the stress energy tensor under the mechanics of perfect fluids, allowing us to lead third party in the case of Newtonian fluids, and in the last part we will see that it is possible to define space-time as a no-Newtonian fluids.

Hamiltonian formalism for perfect fluids in general relativity

1980 ◽  
Vol 21 (10) ◽  
pp. 2785-2793 ◽  
Author(s):  
Jacques Demaret ◽  
Vincent Moncrief
Keyword(s):  
General Relativity ◽  
Hamiltonian Formalism ◽  
Perfect Fluids
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