Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.


Black holes constrain varying constants


There is evidence to suggest that the fine-structure constant, α — a measure of the strength of the electromagnetic interaction between photons and electrons — is slowly increasing over cosmological timescales1,2,3,4. As α = e2/c (where e is the electronic charge, is Planck's constant and c is the speed of light), this would call into question which of these fundamental quantities are truly constant. Here we consider black-hole thermodynamics as a test of which constants might actually be variable, discounting those that could lead to a violation of the generalized second law of thermodynamics.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. Webb, J. K. et al. Phys. Rev. Lett. 82, 884–887 (1999).

    Article  ADS  CAS  Google Scholar 

  2. Songaila, A. & Cowie, L. L. Nature 398, 667–668 (1999).

    Article  ADS  CAS  Google Scholar 

  3. Webb, J. K. et al. Phys. Rev. Lett. 87, 091301 (2001).

    Article  ADS  CAS  Google Scholar 

  4. Murphy, M. T. et al. Mon. Not. R. Astron. Soc. 327, 1208–1222 (2001).

    Article  ADS  Google Scholar 

  5. Barrow, J. D. Phys. Rev. D 59, 043515 (1999).

    Article  ADS  Google Scholar 

  6. Magueijo, J. Phys. Rev. D 62, 103521 (2000).

    Article  ADS  Google Scholar 

  7. Sandvik, H. B., Barrow, J. D. & Magueijo, J. Phys. Rev. Lett. 88, 031302 (2002).

    Article  ADS  Google Scholar 

  8. Bekenstein, J. D. Phys. Rev. D 25, 1527–1539 (1982).

    Article  ADS  CAS  Google Scholar 

  9. Barrow, J. D. & Magueijo, J. Phys. Lett. B 443, 104–110 (1998).

    Article  ADS  CAS  Google Scholar 

  10. Bekenstein, J. D. Phys. Rev. D 9, 3292–3300 (1974).

    Article  ADS  Google Scholar 

  11. Hawking, S. W. Phys. Rev. D 13, 191–197 (1976).

    Article  ADS  Google Scholar 

  12. Magueijo, J. Phys. Rev. D 63, 043502 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  13. Penrose, R. Rev. Nuovo Cimento 1, 252–276 (1969).

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to P. C. W. Davies.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Davies, P., Davis, T. & Lineweaver, C. Black holes constrain varying constants. Nature 418, 602–603 (2002).

Download citation

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing