Erratum to: Gravitons in a Casimir box

Alessio, Francesco; Barnich, Glenn; Bonte, Martin

doi:10.1007/jhep03(2021)228

Cited by 3 publications

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“…The radial component h rr and the cross of angular and perpendicular components h φz for both fields satisfy Dirichlet boundary conditions, while h E,M φr and h E,M zr satisfy Neumann ones. Following the spirit of DeWitt's approach [34], the dynamics of physical gravitons in linearized gravity is equivalent to that of a free massless scalar field on a twice interval [41]. Accordingly, we are allowed to make gravitational analogue of the electromagnetic results and decompose the gravitoelectric and gravitomagetic fields into the parts describing their polarizations and a scalar field that is responsible for the dynamical contributions, respectively,…”

Section: Preliminarymentioning

confidence: 99%

Gravitational Casimir Effect in Inspiralling Neutron Star Binary

Wang¹

2022

Preprint

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Currently, the discussions and investigations for the vacuum energy is drawing great both theoretical and experimental attention. The vacuum states of variety of fields, subject to special boundary conditions, may contribute to non-trivial macroscopic vacuum energy, i.e. the Casimir effect, which become an interdisciplinary subject and plays an important role in a variety of fields of physics. We adopt Schwinger's source theory and study the Casimir effect due to the quantization of gravitation, i.e. the gravitational Casimir effect (GCE), in inspiraling neutron star (NS) binaries with wide separation of 10 9 m. By considering gravitoelectromagnetism (GEM) arising from the spiral-in orbital motion and evaluating the contributions of GEM to the vacuum energy of gravitons radiated during the orbital decay, we demonstrate that, when the orbital separation of the binary decay a distance of L in radial direction, the GEM results in a small Casimir correction to the gravitational vacuum energy, which contributes to an attractive gravitational Casimir force to the binary, in addition the gravitational force. The gravitational waves (GWs), emitted from wide inspiraling NS binaries, locate in the low-frequency band of 10 −4 − 1 Hz. For a characteristic GW frequency of 10 −3 Hz, the gravitational Casimir correction to the signals is estimated as of the order of ∼ 10 −24 , which corresponds to a force of 10 −20 N. By considering that the sensitivity of space-based gravitational wave observatory, LISA/eLISA and Taiji, can be reduced to 10 −24 , we would expect that LISA/eLISA and Taiji with sensitivity improvements give the powerful tool to detect GCE in the near future.

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Section: Preliminarymentioning

confidence: 99%

Gravitational Casimir Effect in Inspiralling Neutron Star Binary

Wang¹

2022

Preprint

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Notes on massless scalar field partition functions, modular invariance and Eisenstein series

Alessio

Barnich

Bonte

2021

J. High Energ. Phys.

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The partition function of a massless scalar field on a Euclidean spacetime manifold ℝd−1 × 𝕋2 and with momentum operator in the compact spatial dimension coupled through a purely imaginary chemical potential is computed. It is modular covariant and admits a simple expression in terms of a real analytic SL(2, ℤ) Eisenstein series with s = (d + 1)/2. Different techniques for computing the partition function illustrate complementary aspects of the Eisenstein series: the functional approach gives its series representation, the operator approach yields its Fourier series, while the proper time/heat kernel/world-line approach shows that it is the Mellin transform of a Riemann theta function. High/low temperature duality is generalized to the case of a non-vanishing chemical potential. By clarifying the dependence of the partition function on the geometry of the torus, we discuss how modular covariance is a consequence of full SL(2, ℤ) invariance. When the spacetime manifold is ℝp × 𝕋q+1, the partition function is given in terms of a SL(q + 1, ℤ) Eisenstein series again with s = (d + 1)/2. In this case, we obtain the high/low temperature duality through a suitably adapted dual parametrization of the lattice defining the torus. On 𝕋d+1, the computation is more subtle. An additional divergence leads to an harmonic anomaly.

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Gravitational observatories

Anninos,

Galante,

Maneerat

2023

J. High Energ. Phys.

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We consider four-dimensional general relativity with vanishing cosmological constant defined on a manifold with a boundary. In Lorentzian signature, the timelike boundary is of the form σ × ℝ, with σ a spatial two-manifold that we take to be either flat or S2. In Euclidean signature we take the boundary to be S2 × S1. We consider conformal boundary conditions, whereby the conformal class of the induced metric and trace K of the extrinsic curvature are fixed at the timelike boundary. The problem of linearised gravity is analysed using the Kodama-Ishibashi formalism. It is shown that for a round metric on S2 with constant K, there are modes that grow exponentially in time. We discuss a method to control the growing modes by varying K. The growing modes are absent for a conformally flat induced metric on the timelike boundary. We provide evidence that the Dirichlet problem for a spherical boundary does not suffer from non-uniqueness issues at the linearised level. We consider the extension of black hole thermodynamics to the case of conformal boundary conditions, and show that the form of the Bekenstein-Hawking entropy is retained.

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Erratum to: Gravitons in a Casimir box

Abstract: The correct name of the second author is Martin Bonte. In the expression for the Pauli-Fierz Hamiltonian in equation (3.10), we missed two terms that vanish on the constraint surface.

Cited by 3 publications

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Gravitational Casimir Effect in Inspiralling Neutron Star Binary

Gravitational Casimir Effect in Inspiralling Neutron Star Binary

Notes on massless scalar field partition functions, modular invariance and Eisenstein series

Gravitational observatories

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