The facts can be found here.

For camera, PDA and cell phone batteries, and most laptop batteries, the only restriction is that spare batteries (not installed in a device) must be in your carry-on.

Details: Lithium-ion rechargeable batteries installed in devices - permitted, up to 300 watt-hours.

Spare lithium-ion rechargeable batteries up to 300 watt-hours: Must be in carry-on baggage. Batteries over 100 watt-hours limited to 2.

All camera, PDA and cell phone batteries, and most laptop batteries, are under 100 watt-hours, so you can take any number of spares but they must be in your carry-on.

The BP-4L battery in the N810 is a big 5.55 watt-hours. It is a lithium polymer battery, which is a type of lithium-ion battery, not a lithium metal battery.

To compute the watt-hours of a battery, multiply the voltage by the mA-hours and divide by 1000.

There are more stringent restrictions on lithium metal batteries (coin batteries, and lithium AA batteries, for example). Spares of these would have to be carry-on, up to 25 watt hours.