Ahmet Baykal
By using the algebra of exterior forms and the first order formalism with constraints, an alternative derivation of the field equations for the Minimal massive 3D gravity model is presented.
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It has recently been pointed out by Finn that the long-standing derivation of the response of an interferometric gravitational wave detector contains several errors. Here I point out that a contemporaneous derivation of the gravitational wave response for spacecraft doppler tracking and pulsar timing avoids these pitfalls, and when adapted to describe interferometers, recovers a simplified version of Finn's derivation. This simplified derivation may be useful for pedagogical purposes.
Alternative Derivation of the Correspondence Between Rindler and Minkowski Particles
我们开发了一个替代的推导Unruh和Wald的开创性的结果，吸收一个Rindler粒子的检测器所描述的均匀加速的观察者对应的闵可夫斯基粒子的发射所描述的惯性观察者。实际上，我们把它颠倒过来，即闵可夫斯基粒子的发射一般对应于林德勒粒子的发射或吸收。
Alternative Derivations of Hawking Radiation
本文综述霍金辐射的隧穿、反常与 Green 函数等替代推导，从不同物理视角揭示黑洞热辐射及相关量子引力特征。
Starting from Plebanski's action for general relativity with cosmological constant, we show that by integrating out all the auxiliary fields Krasnov's action immediately emerges. We also perform the Hamiltonian analysis of the latter and show that the constraints are those of the Ashtekar formalism.
An alternative derivation of the first-order relativistic contribution to perihelic precession is presented. Orbital motion in the Schwarzschild geometry is considered in the Keplerian limit, and the orbit equation is derived for approximately elliptical motion. The method of solution makes use of coordinate transformations and the correspondence principle, rather than the standard perturbative approach. The form of the resulting orbit equation is similar to that derived from Newtonian mechanics and includes first-order corrections to Kepler's orbits due to general relativity. The associated r…
The Barrett-Crane intertwiner for the Riemannian general relativity is systematically derived by solving the quantum Barrett-Crane constraints corresponding to a tetrahedron (except for the non-degeneracy condition). It was shown by Reisenberger that the Barrett-Crane intertwiner is the unique solution. The systematic derivation can be considered as an alternative proof of the uniqueness. The new element in the derivation is the rigorous imposition of the cross-simplicity constraint.
We provide proofs of some assumptions recently made by F. O. Minotti to conclude on the possibility that an additional scalar field minimally coupled to gravity may help to reconcile a Brans-Dicke coupling constant $ω$ of the order unity with solar system bounds.
We show that the recent derivation that triangleland's topology and geometry is $S^2$ from Heron's formula does not extend to quadrilaterals by considering Brahmagupta, Bretschneider and Coolidge's area formulae. That $N$-a-gonland is more generally $CP^{N - 2}$ (with $CP^1 = S^2$ recovering the triangleland sphere) follows from Kendall's extremization that is habitually used in Shape Theory, or the generalized Hopf map. We further explain our observation of non-extension in terms of total area not providing a shape quantity for quadrilaterals. It is rather the square root of of sums of square…
The possibility of detecting the gravitomagnetic clock effect using artificial Earth satellites provides the incentive to develop a more intuitive approach to its derivation. We first consider two test electric charges moving on the same circular orbit but in opposite directions in orthogonal electric and magnetic fields and show that the particles take different times in describing a full orbit. The expression for the time difference is completely analogous to that of the general relativistic gravitomagnetic clock effect in the weak-field and slow-motion approximation. The latter is obtained …
We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from the Newton's law, which is closer in spirit to the thermodynamic description of gravity. As a warm up exercise, we have explicitly demonstrated that projecting the Riemann curvature tensor appropriately and taking a cue from Poisson's equation, the Einstein's equations immediately follow. The above derivation naturally generalizes to Lovelock gravity theories where an appropriate curvature tensor satisfying the symmetries as well as the Bianchi derivative properties of the Riemann tenso…
A new strategy in deriving the Lense-Thirring effect, in the weak field and slow motion approximation of general relativity, on the orbital elements of a test body in the field of different central rotating sources exhibiting axial symmetry is presented. The approach adopted in the present work, in the case of a perfectly spherical source, leads for all the Keplerian orbital elements of the freely falling particle to the well known Lense-Thirring equations. The case of a central nonspherical body is also worked out.
We examine an extension of General Relativity with an explicit non-minimal coupling between matter and curvature. The purpose of this work is to present an overview of the implications of the latter to various contexts, ranging from astrophysical matter distributions to a cosmological setting. Various results are discussed, including the impact of this non-minimal coupling on the choice of Lagrangian density, on a mechanism to mimic galactic and cluster dark matter, on the possibility of accounting for the accelerated expansion of the Universe, energy density fluctuations and modifications to …
Motivated by exploring the interface between thermodynamics of spacetime and quantum gravity effects, we develop a heuristic derivation of Hawking temperature and Bekenstein entropy from the existence of a minimal resolvable area. Moreover, we find leading order quantum gravity corrections to them that are in qualitative agreement with results obtained by other methods, both heuristic and rigorous. In this way, we recover, as a particular case, the corrections heuristically obtained from the existence of minimal length. We also show that the size of minimal area is constrained from above by we…
An alternative derivation of generalized gravitational entropy associated to co-dimension 2 'entangling' hypersurfaces is given. The approach is similar to the Jacobson-Myers 'Hamiltonian' method and it does not require computations on manifolds with conical singularities. It is demonstrated that the entangling surfaces should be extrema of the entropy functional. When our approach is applied to Lovelock theories of gravity the generalized entropy formula coincides with results derived by other methods.
In this paper we show that it is possible to derive the Kerr solution in an alternative, intuitive way, based on physical reasoning and starting from an orthogonal metric ansatz having manifest ellipsoidal space-time symmetry (ellipsoidal symmetry). This is possible because both flat metric in oblate spheroidal (ellipsoidal) coordinates and Kerr metric in Boyer-Lindquist coordinates can be rewritten in such a form that the difference between the two is only in the time-time and radial-radial metric tensor components, just as is the case with Schwarzschild metric and flat metric in spherical co…
The chiral vortical effect (CVE) was derived first for non-interacting massless fermions. Recently, an alternative derivation of the CVE was suggested which relates it to the radiation from the horizon of a rotating black hole. We attempt to generalize the latter derivation to the case of photons and encounter a crucial factor of two difference between the two ways of visualizing the CVE. Reservations and possible explanations are briefly discussed.
Clifford Algebra Derivation of the Characteristic Hypersurfaces of Maxwell's Equations
一个替代的，教学上更简单的推导允许的物理波前的传播电磁信号使用几何代数。麦克斯韦方程组可以用三维克利福德代数（同构于电磁学的泡利代数旋量公式）表示为单个多向量方程。随后，人们可以更容易地解决的时间演变的电场和磁场的同时在三维超曲面上评估的领域。场的时间导数可以是奇异的特殊“特征”表面的形式可以毫不费力地快速推导出来。
Quantum gravitational effects usually are assumed to be important on small scale (Planck scale), but actually these effects are also very significant on large (cosmological) scales. It is recognized that in curved spacetime, the existence of a minimal measurable momentum is inevitable. In this paper, we study thermodynamic properties of the late time universe in the presence of a minimal measurable momentum cutoff that encodes infra-red modification of the underlying field theory. In this regard, we consider a non-relativistic regime and show that the existence of a minimal measurable momentum…
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